%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU151+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:37:46 AM UTC 2026
% Result : Theorem 23.43s 6.88s
% Output : Refutation 23.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 29 unt; 0 typ; 6 def)
% Number of atoms : 191 ( 136 equ; 0 cnn)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 492 ( 79 ~; 67 |; 31 &; 299 @)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 121 ( 6 ^; 99 !; 10 ?; 121 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $o ).
thf(sk6_decl,type,
sk6: $i > $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
? [B: $i,C: $i,D: $i] :
( ( A != D )
& ( A != C )
& ( ( B @ ( A @ unordered_pair ) )
= ( D @ ( C @ unordered_pair ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
? [B: $i,C: $i] :
( ( sk1 != C )
& ( sk1 != B )
& ( ( A @ ( sk1 @ unordered_pair ) )
= ( C @ ( B @ unordered_pair ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
? [B: $i] :
( ( sk1 != B )
& ( sk1 != A )
& ( ( sk2 @ ( sk1 @ unordered_pair ) )
= ( B @ ( A @ unordered_pair ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
( ( sk1 != A )
& ( sk1 != sk3 )
& ( ( sk2 @ ( sk1 @ unordered_pair ) )
= ( A @ ( sk3 @ unordered_pair ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ in ) )
=> ( ( D = B )
| ( D = C ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( D = B )
| ( D = C ) )
=> ( A @ ( D @ in ) ) ) ) ) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( D = B )
| ( D = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(21,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( C
= ( B @ ( A @ unordered_pair ) ) )
=> ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ unordered_pair ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
=> ( ! [D: $i] :
( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(miniscope,[status(thm)],[21]) ).
thf(23,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( F @ ( G @ ( H @ sk7 ) ) @ in ) )
| ( H @ ( G @ ( F @ sk5 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ( ( F @ ( G @ ( H @ sk7 ) ) )
= G )
| ( ( F @ ( G @ ( H @ sk7 ) ) )
= F )
| ( H @ ( G @ ( F @ sk5 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk5 ) ) )
| ( ( F @ ( G @ ( H @ sk6 ) ) )
!= G ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk5 ) ) )
| ( ( F @ ( G @ ( H @ sk6 ) ) )
!= F ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk5 ) ) )
| ( H @ ( F @ ( G @ ( H @ sk6 ) ) @ in ) ) )
& ( ( C @ ( E @ in ) )
| ( E != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( C @ ( E @ in ) )
| ( E != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( D = B )
| ( D = A )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(42,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(43,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( A @ in ) ),
inference(simp,[status(thm)],[42]) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ( D = A )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ in ) )
| ( D = B )
| ( D = A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ unordered_pair ) @ ( C @ in ) )
| ( C = B )
| ( C = A ) ),
inference(simp,[status(thm)],[34]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ unordered_pair ) )
= ( D @ ( C @ unordered_pair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ unordered_pair ) )
= ( D @ ( C @ unordered_pair ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ unordered_pair ) )
= ( D @ ( C @ unordered_pair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
~ ~ ? [A: $i,B: $i,C: $i,D: $i] :
( ( A != D )
& ( A != C )
& ( ( B @ ( A @ unordered_pair ) )
= ( D @ ( C @ unordered_pair ) ) ) ),
inference(miniscope,[status(thm)],[7]) ).
thf(9,plain,
( ( sk1 != sk4 )
& ( sk1 != sk3 )
& ( ( sk2 @ ( sk1 @ unordered_pair ) )
= ( sk4 @ ( sk3 @ unordered_pair ) ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(12,plain,
sk1 != sk4,
inference(cnfConj,[status(thm)],[9]) ).
thf(15,plain,
sk4 != sk1,
inference(lifteq,[status(thm)],[12]) ).
thf(718,plain,
! [C: $i,B: $i,A: $i] :
( ( A != sk4 )
| ( C != sk1 )
| ~ ( B @ ( A @ unordered_pair ) @ ( C @ in ) )
| ( C = B ) ),
inference(paramod_ordered,[status(thm)],[35,15]) ).
thf(719,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ~ ( A @ ( sk4 @ unordered_pair ) @ ( B @ in ) )
| ( B = A ) ),
inference(pattern_uni,[status(thm)],[718:[bind(A,$thf( sk4 ))]]) ).
thf(808,plain,
! [A: $i] :
( ~ ( A @ ( sk4 @ unordered_pair ) @ ( sk1 @ in ) )
| ( sk1 = A ) ),
inference(simp,[status(thm)],[719]) ).
thf(10,plain,
( ( sk2 @ ( sk1 @ unordered_pair ) )
= ( sk4 @ ( sk3 @ unordered_pair ) ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(13,plain,
( ( sk4 @ ( sk3 @ unordered_pair ) )
= ( sk2 @ ( sk1 @ unordered_pair ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ unordered_pair ) )
!= ( B @ ( A @ unordered_pair ) ) )
| ( ( sk2 @ ( sk1 @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,20]) ).
thf(95,plain,
( ( sk3 @ ( sk4 @ unordered_pair ) )
= ( sk2 @ ( sk1 @ unordered_pair ) ) ),
inference(pattern_uni,[status(thm)],[94:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk4 @ unordered_pair ) )
!= ( B @ ( A @ unordered_pair ) ) )
| ( sk2 @ ( sk1 @ unordered_pair ) @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[95,43]) ).
thf(123,plain,
sk2 @ ( sk1 @ unordered_pair ) @ ( sk4 @ in ),
inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( sk4 )),bind(B,$thf( sk3 ))]]) ).
thf(678,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ unordered_pair ) @ ( sk4 @ in ) )
!= ( B @ ( A @ unordered_pair ) @ ( C @ in ) ) )
| ~ $true
| ( C = B )
| ( C = A ) ),
inference(paramod_ordered,[status(thm)],[123,35]) ).
thf(679,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ unordered_pair ) @ ( sk4 @ in ) )
!= ( B @ ( A @ unordered_pair ) @ ( C @ in ) ) )
| ( C = B )
| ( C = A ) ),
inference(simp,[status(thm)],[678]) ).
thf(680,plain,
( ( sk4 = sk2 )
| ( sk4 = sk1 ) ),
inference(pattern_uni,[status(thm)],[679:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk4 ))]]) ).
thf(983,plain,
sk4 = sk2,
inference(simplifyReflect,[status(thm)],[680,15]) ).
thf(3837,plain,
! [A: $i] :
( ~ ( A @ ( sk2 @ unordered_pair ) @ ( sk1 @ in ) )
| ( sk1 = A ) ),
inference(rewrite,[status(thm)],[808,983]) ).
thf(11,plain,
sk1 != sk3,
inference(cnfConj,[status(thm)],[9]) ).
thf(14,plain,
sk3 != sk1,
inference(lifteq,[status(thm)],[11]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ unordered_pair ) )
!= ( B @ ( A @ unordered_pair ) ) )
| ( sk2 @ ( sk1 @ unordered_pair ) @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[13,43]) ).
thf(50,plain,
sk2 @ ( sk1 @ unordered_pair ) @ ( sk3 @ in ),
inference(pattern_uni,[status(thm)],[49:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(512,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ unordered_pair ) @ ( sk3 @ in ) )
!= ( B @ ( A @ unordered_pair ) @ ( C @ in ) ) )
| ~ $true
| ( C = B )
| ( C = A ) ),
inference(paramod_ordered,[status(thm)],[50,35]) ).
thf(513,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ unordered_pair ) @ ( sk3 @ in ) )
!= ( B @ ( A @ unordered_pair ) @ ( C @ in ) ) )
| ( C = B )
| ( C = A ) ),
inference(simp,[status(thm)],[512]) ).
thf(514,plain,
( ( sk3 = sk2 )
| ( sk3 = sk1 ) ),
inference(pattern_uni,[status(thm)],[513:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(952,plain,
sk3 = sk2,
inference(simplifyReflect,[status(thm)],[514,14]) ).
thf(953,plain,
sk2 != sk1,
inference(rewrite,[status(thm)],[14,952]) ).
thf(3848,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk1 != sk1 )
| ~ ( A @ ( sk2 @ unordered_pair ) @ ( sk1 @ in ) ) ),
inference(paramod_ordered,[status(thm)],[3837,953]) ).
thf(3849,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( A @ ( sk2 @ unordered_pair ) @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[3848]) ).
thf(3850,plain,
~ ( sk2 @ ( sk2 @ unordered_pair ) @ ( sk1 @ in ) ),
inference(pattern_uni,[status(thm)],[3849:[bind(A,$thf( sk2 ))]]) ).
thf(954,plain,
( ( sk4 @ ( sk2 @ unordered_pair ) )
= ( sk2 @ ( sk1 @ unordered_pair ) ) ),
inference(rewrite,[status(thm)],[13,952]) ).
thf(1101,plain,
( ( sk2 @ ( sk2 @ unordered_pair ) )
= ( sk2 @ ( sk1 @ unordered_pair ) ) ),
inference(rewrite,[status(thm)],[954,983]) ).
thf(4207,plain,
~ ( sk2 @ ( sk1 @ unordered_pair ) @ ( sk1 @ in ) ),
inference(rewrite,[status(thm)],[3850,1101]) ).
thf(4215,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ ( sk1 @ unordered_pair ) @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,4207]) ).
thf(4216,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ ( sk1 @ unordered_pair ) @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[4215]) ).
thf(4217,plain,
$false,
inference(pattern_uni,[status(thm)],[4216:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU151+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.24/0.49 % Computer : n007.cluster.edu
% 0.24/0.49 % Model : x86_64 x86_64
% 0.24/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.49 % Memory : 8046.5625MB
% 0.24/0.49 % OS : Linux 6.8.0-71-generic
% 0.24/0.49 % CPULimit : 300
% 0.24/0.50 % WCLimit : 300
% 0.24/0.50 % DateTime : Sat Sep 26 08:39:09 UTC 2026
% 0.24/0.50 % CPUTime :
% 0.24/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.97/1.04 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.45/1.25 % [INFO] Parsing done (204ms).
% 1.45/1.27 % [INFO] Running in sequential loop mode.
% 2.38/1.82 % [INFO] eprover registered as external prover.
% 2.38/1.83 % [INFO] Scanning for conjecture ...
% 2.63/1.92 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.63/1.96 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.63/1.97 % [INFO] Problem is first-order (TPTP FOF).
% 2.63/1.98 % [INFO] Type checking passed.
% 2.63/1.98 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 23.43/6.87 % [INFO] Killing All external provers ...
% 23.43/6.88 % Time passed: 6237ms (effective reasoning time: 5596ms)
% 23.43/6.88 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 23.43/6.88 % Axioms used in derivation (2): d2_tarski, commutativity_k2_tarski
% 23.43/6.88 % No. of inferences in proof: 53
% 23.43/6.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6237 ms resp. 5596 ms w/o parsing
% 23.94/6.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.94/6.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------